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Math Help - Kinematics

  1. #1
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    Kinematics

    A car traveling at a constant speed of 33.2m/s passes a trooper hidden behind a billboard at t = -1s. One second later, at t=0, the trooper sets in chase after the car with a constant acceleration of 2.92 m/s/s.

    At what time t does the trooper overtake the speeding car? Answer in units of s.



    For answers I tried 11.39683s and 22.739726s and both were wrong
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vesperka View Post
    A car traveling at a constant speed of 33.2m/s passes a trooper hidden behind a billboard at t = -1s. One second later, at t=0, the trooper sets in chase after the car with a constant acceleration of 2.92 m/s/s.

    At what time t does the trooper overtake the speeding car? Answer in units of s.



    For answers I tried 11.39683s and 22.739726s and both were wrong
    Let's simply start our clock at t = 0 s. I am using a coordinate system where the origin is the point where the car and cop are at t = 0 s, and choose the +x direction in the direction of the velocity of the car.

    So for the car:
    x_0 = 0~m
    v_0 = 33.2~m/s <-- This is constant.
    a = 0~m/s^2

    The position of the car is given as
    x = x_0 + v_0t = 33.2t

    For the cop:
    x_0 = 0~m
    v_0 = 0~m/s
    a = 2.92~m/s^2

    The position of the cop is given as
    x = x_0 + v_0t + \frac{1}{2}at^2 = 1.46t^2

    We want to find where the car and cop meet, so equate these two expressions:
    x = 33.2t = 1.46t^2

    Now solve for t.
    I get t = 0~s (which we already knew) and t = 22.7397~s

    It is possible that the computer didn't accept your second (and correct) answer because you didn't give the result to the proper number of significant digits: t = 22.7 s.

    -Dan
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  3. #3
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    Hmm, I tried 22.7 also and it's still no good. I'll e-mail my teacher and see what he has to say on the issue, this is weird
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by vesperka View Post
    Hmm, I tried 22.7 also and it's still no good. I'll e-mail my teacher and see what he has to say on the issue, this is weird
    I'm curious to see what your teacher has to say about it.

    -Dan
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  5. #5
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    He probably won't respond for a while, but I thought of something.

    The position function of the car is:

    33.2x+33.2

    because at 0 seconds the car is 33.2 meters ahead. I can't come up with a valid position function for the police though. I'm having a bit of a brain block, it seems like there should be a way to find position at any given time knowing only acceleration.

    Would the position function for the police be 1.46x^2 ?

    From this, the velocity would be 2.92X and the acceleration would be 2.92, just like was given.
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  6. #6
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    There we go

    The position of the car is 33.2X + 33.2 and the position of the police is 1.46x^2.

    Then I just found the intersection on the calculator and got 23.699239s as my answer and it worked. Thanks for helping me on this one
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  7. #7
    Forum Admin topsquark's Avatar
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    Ah! I just saw what I did wrong. The cop starts one second later.

    Grrr... And I had consciously thought of that when I started writing the response and forgot it almost immediately. I hate it when that happens!

    -Dan
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